ULTIMATE IMAGE SINGULARITIES FOR EXTERNAL ELLIPSOIDAL HARMONICS.

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Abstract

The image system of singularities of an arbitrary exterior potential field within a triaxial ellipsoid is derived. It is found that the image system consists of a source and doublet distribution over the fundamental ellipsoid. The present contribution is a generalization of previous theories on the image system of an exterior potential field within a sphere and spheroid. A proof of T. H. Havelock's spheroid theorem, which apparently is not available in the literature, is also given. The knowledge of the image system is required, for example, when hydrodynamical forces and moments acting on an ellipsoid immersed in a potential flow are computed by the Lagally theorem. The two examples given consider the image system of singularities of an ellipsoid in a uniform translatory motion and in pure rotation. The results are pertinent to ship hydrodynamics.

Original languageEnglish
Pages (from-to)334-344
Number of pages11
JournalSIAM Journal on Applied Mathematics
Volume26
Issue number2
DOIs
StatePublished - 1974

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